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Gauss: curvature preserved by length-preserving surface development

Contribution grade

Differential geometry · Differential geometry

Reference score300,000Provisional editorial estimate of this exact contribution; its grade is assessed separately.

What changed

The curvature of a regular surface patch is expressed through its metric data, showing that bending preserving those data preserves Gaussian curvature.

Scientific scope

The curvature of a regular surface patch is expressed through its metric data, showing that bending preserving those data preserves Gaussian curvature. This is a local metric-invariance statement, not equality of global shapes or a general embedding theorem. The inspected source is the 1902 translation of the work presented in 1827 and printed in 1828.

Evidence

Source-linked, scoped account of the original work. The published scope states the scientific assumptions and remaining verification limits. WRS has not independently certified the full proof, experimental result or system benchmark.

Contributors

Provisional WRS assessment, edition 2026-10-16.1. Independent expert calibration is pending. This grade does not certify correctness or assign ownership.

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